Atkin-Lehner |
2+ 3+ 5- 31+ 37- |
Signs for the Atkin-Lehner involutions |
Class |
34410d |
Isogeny class |
Conductor |
34410 |
Conductor |
∏ cp |
12 |
Product of Tamagawa factors cp |
deg |
237120 |
Modular degree for the optimal curve |
Δ |
-1914078481612800 = -1 · 219 · 3 · 52 · 312 · 373 |
Discriminant |
Eigenvalues |
2+ 3+ 5- -3 3 1 5 -1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[1,1,0,-48317,-4618179] |
[a1,a2,a3,a4,a6] |
Generators |
[301:2717:1] |
Generators of the group modulo torsion |
j |
-12474916284286514521/1914078481612800 |
j-invariant |
L |
3.7233219066318 |
L(r)(E,1)/r! |
Ω |
0.15965596344413 |
Real period |
R |
1.9434089329287 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
0.99999999999999 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
103230x1 |
Quadratic twists by: -3 |